Computer-aided design (CAD) enables a user to model the complex surfaces of physical real-world objects on a user interface of a computer. Such modeling may involve the computer displaying a basic three-dimensional (3D) shape (e.g., cube or sphere) on the user interface, and the user providing input to the computer to form the 3D shape into the modeled complex surface of the physical real-world object. In order to accurately and efficiently model the complex surface, the user requires use of an input device that provides the user control to form the basic shape into the nonlinear shape of the complex surfaces on the user interface. However, prior input devices allow the user only limited control for inputting the nonlinear shape of the complex surfaces. For example, prior input devices include traditional mouse devices which limit the user to providing linear input in a two-dimensional (2D) plane, as shown in FIG. 1A. Prior input devices further include space mouse devices which do enable the user to provide input in a 3D plane, but still limits the 3D input to linear input, as shown in FIG. 1B. As such, there exists a need in the CAD industry for an input device that provides the user control to accurately and efficiently form the nonlinear shape of a modeled complex surface of a physical real-world object on a user interface.